- Lecture 0 (01/08) Definitions: Categories. Morphisms - injective, surjective, bijective, left/right inverse, isomorphisms. Objects - sub/quotient, initial/final, null.
- Lecture 1 (01/10) Functors. Natural transformations. Equivalence of categories.
- Lecture 2 (01/12) Equivalence of categories cntd. Dual categories. Product of catgories.
- Lecture 3 (01/17) Adjoint functors. Unit and counit of adjunction.
- Lecture 4 (01/19) Adjoint functors cntd. Yoneda's lemma. Representable functors.
- Lecture 5 (01/22) (Functors defining objects). Direct sums and direct products.
- Lecture 6 (01/24) (Functors defining objects). Inverse limit.
- Lecture 7 (01/26) Direct and inverse limits cntd.
- Lecture 8 (01/29) Additive categories. Finite direct sums/products. Kernel and cokernel.
- Lecture 9 (01/31) Kernel and cokernel continued. Abelian categories. Additive functors.
- Lecture 10 (02/02) Notion of exactness: of sequences; of functors. Left/right exact functors. Hom functor.
- Lecture 11 (02/05) Long road ahead - towards derived functors. To do list.
- Lecture 12 (02/07) Injective and projective objects - "effacability".
- Lecture 13 (02/09) Tensor functor. Right exactness.
- Lecture 14 (02/12) Category of complexes. Cohomology functors. Snake lemma.
- Lecture 15 (02/14) Long exact sequence in cohomology. Homotopy.
- Lecture 16 (02/16) Uniqueness (up to homotopy) of injective and projective resolutions.

- Appendix A Grothendieck's axioms (AB3-5) and proof of Baer's criterion of injectivity